JJMIE Jorda Joural of Mechaical ad Idustrial Egieerig Volume, Number, Sep. 007 ISSN 995-6665 Pages 4-55 A Neural Netork Based Real Time Cotroller for Turig Process Bahaa Ibraheem Kazem a, *, Nihad F. H. Zagaa b a Mechatroics Egieerig Dept., b Mechaical Egieerig Dept., Uiversity of Baghdad, Baghdad-Iraq Abstract I this paper, the desig ad implemetatio of a effective eural etork model for turig process idetificatio as ell as a eural etork cotroller to track a desired vibratio level of the turig machie is as a example of usig the eural etork for maufacturig process cotrol. Multi Layer Perceptro (MLP) eural etork architecture ith Leveberg Marquardt (LM) algorithm has bee utilized to trai the turig process idetifier. To differet strategies have bee used for traiig turig process idetifier, ad for traiig the cotroller model, here there is o mathematical model till o could relate the vibratio level to the iput turig process parameters feed, speed, ad depth of cut. The vibratio sigal obtaied by the experimetal ork has bee used to trai a eural etork for idetificatio ad cotrol of the turig process. The developed Neuro cotroller has bee checked by applyig differet referece vibratio sigals here it is foud that the cotroller has good ability to track the referece ithi maximum settlig time that does ot exceed (4 sec for 95% of the sigal); maximum overshot ot exceed (0%) of the referece sigal used for checkig. 007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved Keyords: Real Time Cotrol; Neural Netork; Turiig.. Itroductio The preset goal of maufacturig researches focuses o developig flexible, self adjustig ad uatteded itelliget machie systems. The limited presece of operators at maed machie tools leaves the supervisio, moitorig ad cotrol tasks to computer cotrollers. Although a uatteded machiig process eeds almost o attedace of a operator, tasks such as sesig the effect of process variables ad adjustig the coditios accordigly have to be doe by appropriate sesors ad associated moitors. Oe solutio is to provide o-lie adjustmet of operatig parameters based o sesor iformatio. Systems hich posses such capabilities are referred to as adaptive cotrol AC systems. Actually most machiig adaptive cotrollers are categorized i so-called adaptive cotrol for costraits ACC systems, here the operatig parameters are adjusted so as to maximize productivity hile respectig process costraits like cuttig force or poer limits. I practice, the most importat dra back of ACC is their lack of feed back o part quality here there is o measuremet device that could measure part quality surface fiish i a o lie real time maer. I cotrast adaptive cotrol ith optimizatio ACO systems adjust the operatig parameters so that predefied parameters of performace idex are optimized []. Most ACO systems assumed a detailed process model is available ad complete ith ko aalytical or empirical costat. A great dra back rise here hich is the eed to collect very specialized experimetal ad aalytical data geerally required for model simulatio before its implemetatio i the feed back cotrol scheme. To alleviate some of these problems ad provide the model ad the cotroller ith more itelligece, better fit to oliear behaviour ad capacity of adaptatio over time, eural etorks appear as oe of the most iterestig techiques. I recet years, there as a icrease iterest sho i the utilizatio of eural etorks for various research fields such as robotics, optimizatio, liear ad o-liear programmig, patter recogitio, ad computer visio. This as due to the advaces i eural etork algorithms ad also the availability of fast parallel architectures that are used to cotrol dyamical systems such as machiig systems. The aim is of usig multilayered eural etork composed of feed back ad feed forard cotrollers, ad several learig architectures to trai the eural cotroller i order to provide appropriate iputs to the plat, so the desired respose is obtaied. I compariso ith traditioal adaptive cotroller, their results idicate that eural etork approaches ell i oise elimiatio, ork for liear ad o-liear systems ad ca be implemeted * Correspodig author. e-mail: drbahaa@uob.edu.iq
44 007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) very efficietly for large-scale systems []. The eural etork also used i ide variety of data processig applicatios, here real-time data aalysis ad iformatio extractio is required. A great advatage of eural etork approach is that most of itese computatio takes place durig the traiig process. Oce the eural etork is traied for particular task, operatio is relatively fast ad uko samples ca be rapidly idetified i the field []. Other applicatios such as modelig, idustrial ispectio ad quality cotrol have bee spread i maufacturig field []. Presetatio ad aalysis for computerized umerical cotrol CNC for maufacturig system have bee itroduced by Kore [4]. To types of CNC systems referred to as Referece-Pulse ad Sampled-Data are discussed. I the first system, referece pulses ere geerated by the computer ad supplied to a exteral digital cotrol loop. With the Sampled Data techique, the computer served as a comparator of the cotrol loop ad trasmitted the positio error at fixed time itervals. Fig.. represet block diagram of a Sampled-Data CNC system. Both types had bee aalyzed aalytically ad verified experimetally ad the results ere satisfied. Athai ad Viod [5] proposed several chages o special type of lathe machie used for atch makig. To stepper motors used to drive the carriage ad the cross slide, ad lo cost PC type (Siclair ZX spectrum) used as a cotrol platform. Figure : Architecture of speed ad positio cotrol system for millig process [7] George et al. [8] evolved a sychroizig cotrol algorithm. This algorithm as developed to miimize the trackig error ad the cotourig error ith stroger emphasis o cotourig error. A Itel (486) based AT compatible computer had bee used (applyig this algorithm) to cotrol a (Matsuura MC50V) high speed, (-axis) vertical machiig cetre. A schematic diagram of the cotrol system is sho i Fig.. Figure : Block diagram of a sampled-data CNC system [4] Achi [6] have described the utilizatio of microcomputer to cotrol steppig motor actuated hydraulic servos derivig a to axis millig machie; also a program for iterpolatio purpose developed ad saved i a assembly laguage form i the memory. Altitas ad Peg [7] have made a suggestio ad implemetatio of a program for electroically cotrollig of the speed ad positio associated to feed operatio i a research millig machie. The system mai cosistece ere DC-servomotor (actuator), ecoder (for positio feed back sigal), ad tachogeerator (for velocity feed back sigal). A IBM PC ad iterface card cotroller type (DMC-0 motio cotroller) used. The respose aalysis for system aalytically ad experimetally ere foud close as follos, a (60) Hz as the frequecy operatio bad for velocity loop, (0) ms as the settlig time, ad a steady state error of (0.07fc) fc feed velocity commad. Fig.. represet the architecture of the suggested cotrol system. Figure : Schematic diagram of the cotrol system for -axis vertical machiig cetre [8] Jeffery et al. [9] proposed a cuttig force-moitorig approach. The approach did ot utilize force dyamometers but rather estimates the cuttig forces based o the spidle motor curret ad speed as ell as a model that relates these measuremets to the cuttig force. This method as demostrated o a CNC lathe machie; the empirical tests shoed that the static accuracy as less tha (5%) for the proposed system. For large cuttig forces the accuracy as. reasoable (0dB S/N ratio), hile ith loer cuttig forces the accuracy decreased. Khachustambham ad Zhag [0] developed a itelliget o-lie moitorig system through a eural etork approach. Where the moitorig system detects the cuttig force produced durig the machiig, estimates the tool ear status ad fiish quality from the dyamic variatio of detected cuttig force sigal ad makes a decisio for takig corrective actio he it is eeded.the moitor have bee built o feed forard back propagatioalgorithm. After the traiig of the etork, it had bee applied for cuttig force ad surface fiish moitorig durig the turig of advaced ceramic materials. Fig.4. represets a moitorig system.
007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) 45 Figure 4: Nural et ork Moitorig system for turig process[0] Larse [] have shoed that due to sigificat effects of frictio ad backlash ith turig at lo feed rate i aometric positioig accuracy of machie tool axis especially ith sigificat turig operatio such as diamod turig of glass, ceramic, germaium ad zic sulfide for optical usage. A learig motio cotrol algorithm based o the cereblller model articulatio cotroller eural etork developed for servo cotrol; the learig cotroller as implemeted usig C laguage o a digital sigal processig based apo architecture cotroller or the sigle poit diamod turig machie. Azouzi ad Guillot [] evolved a iverse process eurocotroller implemeted i multilayer feed forard eural etork. O-lie adjustmets of feed rate ad cuttig speed are carried out based o a cost/quality performace idex here the chose performace idex as reachig best quality of product ithi miimal cost hich ere estimated from force ad vibratio sesor measuremets. The simulatio ad experimetal ivestigatios demostrated the effectiveess of eural etork for cotrollig ad optimizig of maufacturig operatios. Applied to a sigle poit turig of a typical fiishig cuttig process, the fial dimesios ad surface fiishes ere foud to be better by (40) ad (80) percet respectively, hile productivity as icreased by (40) percet over the coditios proposed i machiig data hadbooks. Fig.5. demostrates the overall experimetal istallatio. Figure 5: Overall experimetal istallatio for o-lie adjustmets of feed rate ad cuttig speed [] Özel ad Nadgir [] developed to eural etork models, oe as the back-propagatio traiig eural etork ad the other as the back-propagatio predictio eural etork. A traied set of back-propagatio eural etork algorithms used to predict flak ear of cuttig tool ith chamfered ad hoed edge preparatio durig the orthogoal cuttig of hardeed steel ork pieces. The experimet shoed that the eural etork could estimate the flak ear progress very fast ad accurately oce the forces are ko. The percetage error as foud to be (0.59% - 5.09%) betee the measured ad the predicted values of flak ear. Jig et al. [4] proposed a ovel XY positioig table sychroously drive by oe- side dual liear motors. The redudat drive system commoly suffers from sychroous drive precisio problem at high speed ad acceleratio rates. I this paper, the dyamic model of dual liear motors redudat drive system alog X-axis directio is give, ad sychroous drive precisio ca be assured by usig a sychroous cotrol scheme. This scheme has to model referece adaptive cotrollers ad a sychroous error compesator based o eural etorks. Simulatio results are provided to maifest the cotrol system has better static ad dyamic performace ad higher sychroous drive precisio at a mor tha 0g (g = 0.8 m/ s ) high acceleratio profile motio. I this ork, a approach for usig the eural etork for idetificatio ad cotrol of the vibratio sigal acceleratio" as utilized.. Vibratio i Maufacturig Process Vibratio ad chatter of a cuttig tool are complex pheomea, hich, if ucotrolled ca lead to premature tool failure, bad surface fiish, etc. This is particularly importat ith brittle tool materials such as ceramics, some carbides ad diamod. I additio, vibratio affects the mechaical surface ad its itegrity. If excessive, vibratios may eve damage machie tools. Furthermore, the oise geerated may be objectioable, particularly if it is at a high frequecy. Basically, there are to types of vibratio i machiig [].. Forced vibratio: this type of vibratio geerally caused by some periodic force preset i the machie such as that comes from gear drive, imbalace of the machie tool compoets, etc. i machiig process such as millig or turig a shaft ith a key ay or splied shaft, forced vibratios are also caused by the periodic etry ad exit of the cuttig tool. The essetial efforts here is to miimize the vibratio amplitude, sice it cause bad surface fiishig of the ork piece, ad chagig its frequecy far aay from the atural frequecy of the system to prevet the probability of resoace occurrece. Although chagig the cuttig process parameters geerally does t appear to have much ifluece of forced vibratio, chagig the cuttig speed may sometimes help [5]. Chagig the cuttig forces especially the thrust force also ca help [].. Self excited vibratio: these vibratios, called chatter, happe due to the iteractio of the dyamics of the chip removal process ad the structural dyamics of the machie tool. The excited vibratios are usually very high i amplitude ad may cause damage to the
46 007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) machie tool. Chatter typically begis ith a disturbace i the cuttig zoe, such as lack of homogeeity i the ork piece material or its surface coditio ad geometry or a chage i a frictioal coditio at the tool-chip iterface. The most importat type of the self excited vibratio called regeerative chatter, this results from the tool cuttig a surface that has roughess or disturbaces left from a previous cut. Because of the resultig fluctuatios i the cuttig forces the tool is subjected to vibratio ad the process repeated cotiuously, hece the term regeerative. Chagig the operatig parameters, hich geerally iclude feed rate, cuttig speed ad depth of cut, could cotrol the chatter. The eed of makig measuremet of vibratio has arise maily because of the groth of evirometal testig. Specificatio, may a time requires that the equipmet should ithstad stated levels of vibratios. This could be doe quatitatively oly through vibratio measuremets. Vibratio measuremets are frequetly carried out o rotatig ad reciprocatig machiery for aalysis, desig ad trouble shootig purposes. Much koledge has bee gaied i the recet years ad computer solutios of various vibratio problems have bee developed [6]. Hoever, may a time it becomes essetial to make actual measuremets of vibratio characteristics by test durig developmet, either o the machie itself or o its prototype because of the fact that it is difficult to build a perfect mathematical model ith all its iterrelatioship ad complexity. The most familiar istrumet used for vibratio measuremets is the accelerometer. This istrumet is commercially available i a ide verity of types ad rages to meet correspodig diverse applicatio requiremets. The basis for this popularity lies i the folloig features [7]:. Frequecy respose is from zero to some high limitig value. Steady acceleratios ca be measured (except i piezoelectric type).. Displacemet ad velocity ca be easily obtaied by electrical itegratio, hich is much preferred to differetiatio.. Measuremet of trasiet (shock) motio is more readily achieved tha ith displacemet or velocity pickups. 4. Destructive forces i machiery are related more closely to acceleratio tha velocity or displacemet. Piezoelectric accelerometer is idely used for shock ad vibratio measuremets. I geeral, it does t give output for costat acceleratio because of the basic characteristics of piezoelectric motio trasducer, but it do have large output voltage sigal, small size, ad ca have very high atural frequecy. No dampig is provided, ith material hysteresis beig the oly source of eergy loss. This result i a very lo (about 0.0) dampig ratio, but this is acceptable because of the very high atural frequecy. The desig details of piezoelectric accelerometers ca emphasize selected features of performace desired for particular applicatio; o sigle cofiguratio is ideal for all situatios sice tradeoffs exit here just as i all egieerig desig. Several desigs have bee developed for piezoelectric accelerometer ad oe of the most iterested desig scheme is the delta shear, shear desig use bolted stacks of flat plate elemet has bee itroduced recetly to gai further improvemet i performace [7].. Aalysis Of Vibratio Sigal Oe of several quatities that could be used to describe the vibratio effects is peak value either it is displacemet, velocity, or acceleratio form of vibratio, o the other had, more complex vibratios are beig studied other descriptive quatities may be preferred. Oe of the reasos for this is that the peak value describes the vibratio i terms of a quatity, hich depeds oly upo a istataeous vibratio magitude regardless of the time history producig it. A further descriptive quatity that does take the time history ito accout is the Root Mea Square (RMS) value ad could be formulated as X RMS = T T 0 X ()dt t X : The RMS value of the vibratio sigal. RMS T : Period of vibratio sigal. ; t : Time (sec). The importace of RMS value comes from its simple relatioship to the poer cotet of the vibratio, eve ith more complex form of vibratio sigal such as radom oe; it ill be suitably meaigful take the RMS value of the sigal [8]. Fig.6. represets a radom vibratio sigal. X Figure 6: Radom vibratio sigal Some tests have bee doe to esure the radomess of the vibratio sigal by comparig some of its statistical iformatio ith those of a periodic si ave sigal. The tests results are sho i table() & Fig.(7). Table : sie ave ad radom vibratio sigal statistics data Statistical data Sie ave sigal Radom sigal t Mea 0.0456 0.87 STD 7.0698 5.807 RMS 7.048 5.7876 ()
007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) 47 Figure 7: Sie ave ad radom vibratio sigal tests results.. Vibratio Sigal Acquisitio It as foud that the selected accelerometer type (470) as suitable for our applicatio sice it has acceleratio measuremet rage of (0.000 0000) m/s ad a voltage sesitivity of (8.5) mv/ms -... Sigal Amplificatio Sice the vibratio sigal produced by the accelerometer is too small to be read directly by the A/D coverter ad by the PC parallel port, the sigal should be elarged usig a special type of amplifiers called istrumetatio amplifier. Those amplifiers have special properties such as its high iput impedace, lo oise, ad moderate badidth [7]. Those properties have bee satisfied usig a coditioig amplifier type (66) [9]... Calibratio Process Sice the measuremet system is ofte made up of a chai of compoets, each of hich is subject to idividual iaccuracy, it ill be importat to ko ho these iaccuracies may affect the over all system measuremet precisio. The most commo method to do this is to fid the least square criterio, hich miimizes the sum of the squares of the vertical deviatios of the data poits from the fitted lie. The algorithm explaied briefly i the appedix C for sigle compoet. But for chai of compoets, the collected iformatio of each idividual compoet calibratio should be take ito cosideratio accordig to a specified procedure [7]. Assume a case here a computig quatity K. K = f u, u, u,..., u ) ( ()
48 007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) K : Ko fuctio of the idepedet variables u, u, u,..., u. The u' s are the measured quatities (istrumet or compoet outputs) ad are i error by ± Δu, ±Δu, ±Δu,..., ± Δu, respectively. These errors ill cause a error Δ K i the computed result K. The Δ u' s may be cosidered as absolute error. ( u ± Δu u ± Δu, u ± Δu ± Δ ) K ± ΔK = f,,..., u u () By subtractig K i equatio () from K ± ΔK i equatio (), e fially obtai ± ΔK hich is eedlessly time cosumig procedure; hoever a approximate solutio valid for egieerig purposes may be obtaied by applicatio of the Taylor series. Expadig the fuctio f i a Taylor series, e get E arss Assume ± S E limits, arss could be evaluated as follos. 0.5 = ( * 0.00494* 0.97) + ( * 0.46*0.95) = 0. 46 Percetage iaccuracy = E arss 0.5 * 00% = *00% = 5% full scale 0 Fig.8, ad Fig.9. Sho part oe ad part to calibratio curve fittig figures respectively. f ( u ±Δu, u ± Δu, u ± Δu,..., u ± Δu ) = f ( u, u, u,..., u ) Δu +Δu + Δu +... + Δu + ( Δu ) +...... f + + (4) I actual practice, the Δu' s ill all be small quatities ad thus terms such as ( Δu ) ill be egligible. The equatio (4) may be give approximately as Figure 8: Accelerometer calibratio f ( u + Δu, u + Δu, u + Δu,..., u + Δu ) = f ( u, u, u,..., u ) Δu + Δu +... + Δu So absolute error Ea is give by + (5) Ea = ΔK = Δu + Δu + Δu +... + Δu u u u u (6) Whe the Δ u' s are cosidered ot as absolute limits of error, but rather as statistical bouds such as ± S limits. The equatio (6) modified to the root sum square (rss) formula. E arss = Δu + Δu + Δu +... + Δu (7) the measuremet system cosists of to major parts. The first part (accelerometer ad charge amplifier), ad the secod part (iterface card ad host PC). Our idividual calibratio process for parts oe ad to of the measuremet system shos the folloig results. First part curve-fittig equatio y = 0. 97x, S = 0. 00494 Secod part curve-fittig equatio y = 0.95x 0.06, S = 0. 46 Where S is the stadard deviatio value STD Figure 9: AC sigal calibratio 4. Experimetal Cuttig Test The experimetal tests accomplished usig turig machie, ad the cuttig tool used for the process as HSS ith medium carbo steel as a ork piece. The tests have bee doe ith a costat depth of cut equal to (0.6mm), ith o coolig fluid. Fig.0. demostrates the experimetal ork layout. Table.. shos the statistical iformatio obtaied at each cuttig process. Figs -4 sho some experimetal readig for the acceleratio at cuttig tests.
007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) 49 Coditioa l Host PC Work piece Accelerometer Figure 0: Experimetal ork layout Table : Statistical iformatio obtaied by experimetal ork Test Speed Feed (rpm) (mm/rev) RMS Mea STD 540 0.0 4.9767-0.040 4.9794 540 0.04 4.886 0.680 4.886 540 0.05 4.906-0.0444 4.9 4 540 0. 5.4808 0.0 5.4756 5 540 0.06 4.7578-0.058 4.7604 6 60 0.06.7975 0.006.7997 7 60 0.0 5.99 0.867 5.48 8 60 0.04 5.7 0.09 5.47 9 60 0.05 5.0697 0.848 5.0579 0 60 0.08 5.07 0.794 5.967 70 0. 5.0680 0.484 5.0687 70 0.08 4.854 0.65 4.84 70 0.06 4.90 0.86 4.50 4 70 0.04 4.405 0.060 4.4077 5 70 0.0 4.08 0.876 4.07 6 5 0.06.704 0.8.6955 7 5 0.08.4407 0.07.44 8 5 0..9997-0.069.00 9 5 0.04.85 0.664.6 0 5 0.05.07-0.06. 80 0.05.8 0.060.850 80 0.08.96 0.046.965 80 0.06.7079-0.04.709 4 80 0..0 0.066.08 5 80 0.04.654-0.8.67 6 80 0.0.9496-0.0.9484 7 85 0..6-0.04.7 8 85 0.08.97-0.0454.945 9 85 0.06.87 0.0987.77 0 85 0.04.6 0.0.8 Figure : Test (No. 6) Acceleratio (m/s ) Figure : Test (No.0) Acceleratio (m/s ) Acceleratio (m/s ) Figure 4: Test (No.7) Figure : Test (No.4)
50 007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) 5. Netork Architecture Commoly oe euro, eve ith much iput, may ot be sufficiet. A eed for more complicated etork architecture arises that serve as multi euros operatig i parallel i hat is called layer. Sometimes multi layers are more poerful tha the sigle layer etork. For istace, a to-layer etork havig a sigmoid trasfer fuctio i the first layer ad a liear trasfer fuctio i the secod layer ca be traied to approximate most fuctios arbitrarily ell [0]. For more demostratio Fig.5. shos to-layer etork. procedure for modifyig the eights ad biases of a etork i order to trai the etork to perform some task [0]. 6.. Geeral Architecture Selectio Oe of the problems that occur durig eural etork traiig is called overfittig. The error o the traiig set is drive to very small value, but he e data is preseted to the etork the error becomes large. The etork has memorized the traiig examples, but it has ot leared to geeralize to e situatio. Oe method for improvig etork geeralizatio is to use a etork that is just large eough to provide a adequate fit. The larger the etork, the more complex the fuctios the etork ca create. If e use a small etork, it ill ot have eough poer to over fit the data. Ufortuately, it is difficult to ko before had ho large a etork should be for a specific applicatio. 6.. Data Pre Processig Neural etork ca be made more efficiet if certai preprocessig steps are performed o the etork iputs ad targets. This subsectio describes some commo processig techiques that could be used to make traiig process more effective. 6.. Process Depedecy o Mi ad Max of Data Values Figure 5: To layer etork arcitecture It ill be more coveiet to describe the iput/output mathematical relatioship i matrix form, here: ( ( ) { b }) a = [ ] f [ ] { p} + { b } a a a or f +,,, = f, f,,,,,,,,,,, (8), p b b + +, p b b, p b b (9) I spite of existece of several other etork architecture, that could be useful for a lot of applicatios, ad it has bee used i this research. 6. Neural Netork Traiig It is importat o to ko ho the eights ad biases of a etork could be determied. With complex etork, havig may iputs ad complicated architecture, the traiig algorithms solve this problem. The traiig algorithms (learig rules) could be defied as a Before traiig, it is useful to scale iputs ad targets so that they alays fall ithi a specified rage. This process makes the data fall i the rage [-, ]. After the completio of traiig process the etork out put should be coverted back ito its origial uits that ere used for the origial targets. 6.4. Process Depedecy o Mea ad STD of Data Values The origial etork iputs ad outputs are give i the matrices p ad t respectively. The ormalized iputs ad targets that are retured ill have zero mea ad uity stadard deviatio. Also the etork outputs should be coverted back to the origial uits of the targets. The data pre processig used for the data depeds o ormalizig it accordig to data s maximum ad miimum values. This process carried out for both iput feed, speed vector ad output vibratio RMS vector. Equatio 0 shos the ormalizatio equatios. ( p mi p) ( ) p = max mi p p (0) Where p : Iput matrix p : Normalized iput matrix. mi p, max p : Miimum ad maximum iput value i the matrix.
007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) 5 6.5. Data Post Processig Aalysis The performace of a traied etork ca be measured o some extet by the errors o the traiig. But it is ofte useful to ivestigate the etork respose i more detail. Oe optio is to perform a regressio aalysis betee the etork respose ad the correspodig targets. The process ill retur three parameters. The first to parameters, (m ad b), correspod to the slope ad the y itercept of the best liear regressio relatig targets to the etork outputs. The third variable that retured by the post processig is the correlatio coefficiet (R value) betee the outputs ad the targets. It is a measure of ho ell the variatio i the output is explaied by the targets. If this umber is equal to (), the there is perfect correlatio betee the targets ad outputs []. perceptro MLP make it a popular choice for modelig oliear systems ad for implemetig geeral-purpose oliear cotroller The folloig describes the process of desig of the eural etork cotroller. There are typically to steps that ivolved he usig eural etork for cotrol.. System idetificatio.. Cotrol desig. 7. Neuro Cotroller Most of the euro cotrol schemes developed util o are based o the folloig desig approaches [0]. Series cotrol scheme: the eural etork directly lears the mappig from the desired referece sigal to the cotrol iputs, hich yields these sigals. Parallel cotrol scheme: a eural etork is used to compesate the cotrol sigal hich is provided by covetioal cotroller such that the plat output ca track the desired output as close as possible. Self tuig cotrol scheme: a eural etork tues the cotrol parameters icludig the covetioal cotroller such that the plat output follos the desired output sigal as much as possible. Emulator ad cotroller scheme: it maximizes some measure of utility or performace over time, but ca t efficietly accout for oise ad ca t provide real time learig for slo covergece, also ko as backpropagatio - through - time. The self tuig cotrol scheme has bee used i this research ad it is explaied as follos. 7.. Self - Tuig Neuro Cotrol Scheme The self tuig euro cotrol scheme is illustrated i Fig.6., here a eural etork is used to tue the parameters of a covetioal cotroller similar to adjustmet made by a huma operator. The process eed that the huma operator has a moderate amout of experiece ad a great koledge o the cotrol system, hoever, ulike the computer, it is rather impossible for the operator to store past data history of the system for ay kid of operatig coditio. If oe ca iclude the experiece ad the koledge of the operator ito a eural etork ad trai it based o the past data history, the the traied eural etork could be used as meas to tue the cotroller parameters i a o lie ay[]. 8. Desig of the Self - Tuig Neuro - Cotroller Neural etork has bee applied very successfully i the idetificatio ad cotrol of dyamic systems. The uiversal approximatio capabilities of the multilayer Figure 6: tuig euro cotrol scheme 9. Desig of the Self - Tuig Neuro - Cotroller Neural etork has bee applied very successfully i the idetificatio ad cotrol of dyamic systems. The uiversal approximatio capabilities of the multilayer perceptro MLP make it a popular choice for modelig oliear systems ad for implemetig geeral-purpose oliear cotroller The folloig describes the process of desig of the eural etork cotroller. There are typically to steps that ivolved he usig eural etork for cotrol.. System idetificatio.. Cotrol desig. As described previously i system idetificatio stage, a model for the system at to be cotrolled should be developed. I cotrol stage the developed model should be used i traiig the cotroller. This cotroller uses a eural etork model to predict future plat resposes to potetial cotrol sigals. A optimizatio process the computes the cotrol sigal that optimizes the future plat performace. The predictive cotrol process is based o recedig horizo techique. The eural etork model predicts the plat respose over a specified time horizo. The predictios are used by a umerical optimizatio process to determie the cotrol sigal that miimizes the performace criterio equatio () over the specified horizo. Fig..7. demostrates the cotroller optimizatio procedure. This cotroller has bee desiged ad used for this ork. Z N = u ( yr ( t + j) ym ( t + j) ) + ρ ( u' ( t + j ) u' ( t + j ) ) j= N j= N () Z : Optimizatio performace idex. N, N, N : The horizos over hich the trackig error u ad the cotrol icremets are evaluated. u ' : The tetative cotrol sigal Tetative Feed ad Speed Values. y : The desired respose Desired Vibratio RMS Value. r
5 007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) y : The etork model respose Vibratio RMS Value m Developed by the Model. ρ : Factor determies the cotributio that the sum of the square of the cotrol icremets has o the performace idex. Figure 8: Cotroller model traiig process Figure 7: optimizatio procedure 0. Result ad Discussio The desiged cotroller has bee used to cotrol turig process idetifier by applyig differet referece sigals to it as test iputs, to fid out its ability to follo the desired respose; the cotroller is fed by the referece sigals, hich ere the vibratio RMS values, ad the resposes that have bee sho o the scope. The cotroller here is desiged to geerate the values of the feed ad the speed ad the the eural etork turig process idetifier maps it ito vibratio RMS values, the cotroller reads back the output sigal ad compare it to the sigal results from its eural etork model here the optimizatio algorithm update the cotrol actio (feed, speed) sigals so that the turig process idetifier follo the required referece sigal. Fig8. Demostrate the cotroller model traiig process. The learig rate (α ) set to (0.75), ad cotrol process maximum error set to (*0 - ), hich make the traiig process reached to the specified goal at (99) epoch. The desiged cotroller model has bee traied by the backpropagatio algorithm described i chapter four, it cosist of to layer perceptro eural etork ith eight euro i the hidde layer ad oe euro at the output layer. The cotroller model desiged ith tasig activatio fuctio i the hidde layer ad pureli activatio fuctio i the output layer. Fig.9. shos the turig process cotroller. The optimizatio for process cotrol is simulated by the flochart sho i Fig.0. Differet referece sigals have bee used for testig the respose of the cotroller.the first as for iput referece equal to 5, the secod as for iput referece 4.5 for the first to secod ad the the referece decreased to.5. The fial case as the respose of the cotroller for iput referece sigal started ith.5 ad the icreased to 4. The sampled time used as (0.0 sec 00 sample = sec ). Figure 9:Turig process cotroller Set iitial parameters ( Z, N, N, N, ρ, u y, r Apply referece Check output Figure 0: Optimizatio flochart u ' ) Optimize for the specified time & cotrol horizo Update ( u ' ) The desig of system idetifier shos precise results ith (0euro), here the traiig performace idex set to (*0-8 ) as MSE of the output of the eural etork ad the traied etork met that goal sice the error betee the eural etork output ad the targets did ot exceeds (.55*0-4 ). For the desiged eural etork cotroller, it is foud that the cotroller track the referece sigals set, here settig the referece sigal to (5) as acceleratio RMS value as sho i fig.. made the cotroller after a startig ith a iitializatio values of the feed ad the speed be chaged. For referece sigal equal to (5) the cotroller adapts e feed ad speed values 0.095mm/rev, ad 440RPM respectively, this adaptatio completes after (00samples = sec) settig time ad the respose progresses ith a steady state error that does t exceeds (8%) of the referece sigal due to the fluctuatig speed value. To differet referece sigals have bee set to check the ability of the cotroller to track these specified
007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) 5 referece sigals as sho i Fig., here settig of the referece sigal to (4.5) as acceleratio RMS value made the cotroller adapt e feed ad speed values equal to 0.085 mm/rev ad 440 RPM respectively, the cotroller reaches to the specified referece after (00 samples = sec) settlig time. The e referece sigal (.5) has bee tracked by the cotroller after (400samples = 4sec) as settlig time ad the adapted feed ad speed values ere 0.07mm/rev ad 70RPM. Fially e to referece sigals (.5,4) have bee set as acceleratio values as sho i Fig.., the cotroller chages it iitial values (feed = 0.05 mm/rev, speed = 70 RPM) to 0.068 mm/rev ad 0 RPM to reach the referece sigal ithi (00samples = sec). Those referece sigals trackig process that have bee achieved by the Neuro - cotroller sho the ability of the cotroller to track the referece sigal ith miimum settlig time equals to (00samples = sec) ad maximum settlig time equals to (00samples = sec) ad a maximum overshot for the test sigals that does t exceeds (0%) of the referece sigals. Fig., Fig., ad Fig. sho that icreases the value of referece (acceleratio RMS) ot ecessarily leads to icrease the cotrol sigal (Feed, Speed) either decrease it should decrease the cotrol sigal. Acceleratio RMS (m/s ) Acceleratio RMS (m/s ) Figure : Cotroller respose (iput referece = 5) Figure : Cotroller respose (iput referece = 5)
54 007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665). Coclusio I this ork, the effectivess of usig eural etorks as idetificatio ad as a alterative to adaptive cotroller of metal cuttig process are iverstigated. Also, usig the eural etork for system idetificatio releases the cotroller desiger from the problem of modelig complex real systems ad the cofusig related to selectio of the least sigificat system variables hich ca be igored. traiig algorithm for system idetificatio ith high degree of accuracy, hile the traditioal Back propagatio algorithm ca be used to trai eural etorks ith greater error alloace. The cotroller proposed i the curret ork follo the desired respose ith cotrol actios (Feed, Speed) ot metioed i the traiig data ad this make the eural etork has a advatage i beig ork as itelliget map. Fe practical experimets used for traiig the eural etork (idetifier, cotroller) may cover the process ith less error ad this ill miimize the efforts of achievig a lot of practical experimets if compared ith the other traditioal cotrollers. Refereces Acceleratio RMS (m/s ) Figure : Cotroller respose (iput referece =.5,4) The usig of LM (Leveberg-Marquardt) traiig algorithm o the MLP etork eve ith its property of eedig to large memory is successful algorithm i miimizig the traiig error, hich makes it good [] M. P. Groover Fudametal of moder maufacturig process. by Pretice Hall Iteratioal Ic.996. [] P. Tai, H. A. Ryaciotaki, ad D. Hollaay Neural etork implemetatio to cotrol system. A survey of algorithms ad techiques. Trasactio of IEEE, Vol.5, No.,-7, 99. [] P. E. Keller, R. T. Kouzes, L. J. Kagas, ad S. Hashem Neural etork based system for maufacturig applicatio. A paper represeted at the advaced iformatio system ad techology coferece i Williamsburg, VA, USA (8-0) March (994). [4] Y. Kore Desig of computer cotrol for maufacturig system. Trasactios of the America society of mechaical egieerig (ASME), Vol.0, 979. 6-. [5] V.V. Athai ad H. N. Viod A CNC system for a lathe usig a lo cost PC. Computers i idustry, Vol. 7, PP. 47-44, 986. [6] P. U. Achi A lo cost computer umerical cotrol machie system usig LSI iterfaces. IEEE trasactios o idustrial electroics, Vol. 4, No., 987. [7] Y. Altitas ad J. Peg Desig ad aalysis of a modular CNC system. Computers i idustry, Vol., 990. 05-6. [8] T. George, C. Chiu, ad M. Tomizuka Coordiated positio cotrol of multi-axis mechaical system. Joural of dyamic systems, measuremet, ad cotrol, 998. (89-9). [9] L. Jeffery, H. Stei, ad K. Huh Moitorig cuttig forces i turig: A model based approach. Vol. 4, 00. 6- ; ASME. [0] R. G. Khachustambham, ad G. M. Zhag A eural etork approach to o - lie moitorig of a turig process, Trasactio of IEEE, Vol., No.5, 99.07-. [] L.G. Ala Neural etork servo cotrol for ultra-precisio machiig at extremely lo feed rate. PhD Thesis, Uiversity of Illiois at Chicago, 996. [] R. Azouzi ad M. Guillot O-lie optimizatio of the turig process usig a iverse process eurocotroller. Joural of Maufacturig Sciece ad Egieerig, Vol. 0, 998,0-08. [] T. Özel ad A. Nadgir Predictio of a flak ear by usig back- propagatio eural etork modelig he cuttig hardeed H- steel ith chamfered ad hoed CBN tools Iteratioal joural of machie tools & maufacturig desig research ad applicatio, 00. [4] Jeg Che, Qiag Liu ad Chag Qi A Sychroous Drive Cotrol Scheme Based o Neural Netorks for a Novel XYtable Proceedigs of the IEEE Iteratioal Coferece o Automatio ad Logistics August 8 -, 007, Jia, Chia [5] S. Kalpakjia Maufacturig Egieerig ad techology 4 th editio, by Pretice Hall Iteratioal Ic, 00.
007 Jorda Joural of Mechaical ad Idustrial Egieerig. All rights reserved - Volume, Number (ISSN 995-6665) 55 [6] A. K. Sahey A course i mechaical measuremets ad istrumetatio. Secod editio 995, by Dhapat rai ad sos. [7] E. O. Doebeli Measuremet systems applicatio ad desig Fourth editio 990, by McGra Hill publishig compay. [8] J. T. Broch Mechaical vibratio ad shock measuremets. First editio 980, K. Larse & So A/S for publishig. [9] Brüel & Kjaer corporatio Piezoelectric accelerometer ad vibratio preamplifier had book. K. Larse & So A/S for publishig, 978. [0] M. T. Haga, H. B. Demuth, ad Mark Beale Neural etork desig. First editio 996, McGra - Hill publishig compay. [] S. Omatu, M. Khalid, ad R. Yusof Neuro cotrol ad its applicatios. Spriger publishig compay, 994. [] O. Omidvar ad D.L. Elliot Neural system for cotrol., Spriger publishig compay, 997. [] D. T. Pham ad L. Xig Neural etorks for idetificatio, predictio, ad cotrol, Spriger publishig compay, 997.